The 8th common term of the series $S_1 = 3 + 7 + 11 + 15 + 19 + \ldots$ and $S_2 = 1 + 6 + 11 + 16 + 21 + \ldots$ is ______.
Step-by-Step Solution
Key Concept: The common terms form an AP with first term = LCM of common differences away from the first common term. First common term = 11, common difference = LCM(4, 5) = 20.
$S_1$: first term 3, $d=4$. $S_2$: first term 1, $d=5$. First common term: 11. Common difference of common terms: LCM(4,5)=20. $T_8 = 11 + 7 \times 20 = 151$.
Correct Answer: 151